Low density parity check irreducible Goppa codes

Abstract

In this paper, whose earlier version was presented at SAMSA 05 conference, we present some of the results obtained in the on-going research on low density parity check (LDPC) irreducible Goppa codes. The objective of the research is to find irreducible Goppa codes with sparse parity check matrices to which LDPC decoding can be applied. If such codes are found then they would permit efficient encoding and decoding algorithms. We use two methods to come up with a sparse parity check matrix. The first method involves changing the basis of the splitting field of the Goppa polynomial. In the other method, we build the parity check matrix using low weight codewords in the dual code of the Goppa code.